Problem: Simplify the following expression: $\sqrt{28}-\sqrt{63}+\sqrt{112}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{28}-\sqrt{63}+\sqrt{112}$ $= \sqrt{4 \cdot 7}-\sqrt{9 \cdot 7}+\sqrt{16 \cdot 7}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{7}-\sqrt{9} \cdot \sqrt{7}+\sqrt{16} \cdot \sqrt{7}$ $= 2\sqrt{7}-3\sqrt{7}+4\sqrt{7}$ Finally, simplify by combining the terms. $= ( 2 - 3 + 4 )\sqrt{7} = 3\sqrt{7}$